A standard 1 kilogram weight is a cylinder 48.5 mm in height and 52.0 mm in diameter. What is the density of the material?
density=mass/volume=1kg/(PI*.026^2*.0485)
To find the density of the material, we need to know the mass and volume of the cylinder. Since we are given the weight of the cylinder and not the mass, we need to convert the weight to mass.
1 kilogram is equivalent to 1000 grams.
So, the mass of the cylinder is 1000 grams.
Next, we need to calculate the volume of the cylinder using its dimensions.
The formula to calculate the volume of a cylinder is:
Volume = π * (radius)^2 * height
Given that the diameter is 52.0 mm, the radius is half of that:
Radius = 52.0 mm / 2 = 26.0 mm
Converting the radius to meters:
Radius = 26.0 mm / 1000 = 0.026 meters
The height of the cylinder is 48.5 mm, which is:
Height = 48.5 mm / 1000 = 0.0485 meters
Now, plugging in the values into the volume formula:
Volume = π * (0.026)^2 * 0.0485
Using the value of π ≈ 3.14159, we can calculate the volume:
Volume = 3.14159 * (0.026)^2 * 0.0485
Calculating this expression gives the volume in cubic meters.
Finally, we can find the density by dividing the mass by the volume:
Density = Mass / Volume
To find the density of the material, we need to use the formula:
Density = Mass / Volume.
Since we are given the dimensions of the weight and the weight is made of a material with uniform density (assuming), we can calculate the volume of the weight.
The volume of a cylinder can be calculated using the formula:
Volume = π * r^2 * h,
where:
- π represents the mathematical constant pi (approximately 3.1415),
- r is the radius of the cylinder (half of the diameter),
- h is the height of the cylinder.
Given that the diameter of the weight is 52.0 mm, the radius (r) would be half of that, which is 26.0 mm or 0.026 m. The height (h) is given as 48.5 mm or 0.0485 m.
Using the formula for the volume of a cylinder, we can do the calculations as follows:
Volume = π * (0.026)^2 * 0.0485
Now, since the weight is given to be 1 kilogram, which is equivalent to 1000 grams, we can convert the mass to kilograms:
Mass = 1 kg.
Now that we have the mass and volume, we can calculate the density:
Density = Mass / Volume.
Density = 1 kg / Volume.
By substituting the values we calculated for Volume and Mass, we will find the density of the material.